You asked a question about a specific video, and the DVD quality. I'd trust Richard's answer as he's reliable, know's a ton about Star Trek, and somehow has a full copy of the video (ahem).
Encompassed in your question is if it's "lowD" or "Normal."
What I can tell you is that video resolution is just one component of whether or not the picture quality is good to the viewing eye or not. Lighting, steady camera hand, quality of the processing chip(s) in the camera, etc. can often times be more important then just overall resolution. I'm sure you've gone onto youtube for example, and selected a 1080 video with horrible picture quality, and watched a different video shot in 480 that looked better (clearer, crisper, etc.).
Refresh rate is also a factor in video quality which I won't go into here.
As for whether the DVD is better, there are several things to consider.
A standard DVD player, without upscaling, can output video resolution at 720x480 (480i). This was the original DVD standard resolution.
A progressive scan DVD player, without upscaling, can output 720x480 (480p - progressive scan) video signals. This came out second. Interlaced or Progressive has to do with how the lines are painted on the screen, whether it skips every other line then doubles back or draws them sequentially.
480i represents 720 pixels displayed across a screen horizontally and 480 pixels down a screen vertically. This arrangement yields 480 horizontal lines, which are, in turn, displayed alternately. In other words, all the odd lines are displayed, followed by all the even lines.
480p represents 720 pixels displayed across the screen horizontally and 480 pixels down the screen vertically. This arrangement yields 480 horizontal lines on the screen, which are, in turn, displayed progressively, or each line displayed following another.
The Upscaling Process:
Upscaling is a process that mathematically matches the pixel count of the output of the DVD signal to the physical pixel count on an HDTV, which is typically 1280x720 (720p) or 1920x1080 (1080i or 1080p).
720p represents 1,280 pixels displayed across the screen horizontally and 720 pixels down the screen vertically. This arrangement yields 720 horizontal lines on the screen, which are, in turn, displayed progressively, or each line displayed following another.
1080i represents 1,920 pixels displayed across a screen horizontally and 1,080 pixels down a screen vertically. This arrangement yields 1,080 horizontal lines, which are, in turn, displayed alternately. In other words, all the odd lines are displayed, followed by all the even lines.
1080p, on the other hand, represents 1,080 horizontal lines displayed sequentially. This means all lines are displayed during the same pass. 1080p is the highest quality HD display format. There are newer formats now though followed by the letter "K."
All of these resolutions are simply a number of the maximum potential number of pixels that can be displayed. If you shoot in 1080 with a crappy phone camera, in low light conditions, with a lot of motion, as well as a jerky camera, odds are the quality will suck. Whereas with a professional SD camera, with three separate chips for color, good lighting source located behind the camera, on a tripod or with a professional camera man at the helm, etc. The standard definition video will look much better than the HD to the viewer in this scenario.
640 x 352 is normally DIVX IMO, which can give you a clean crisp video if shot right. I'm not sure if a 640 x 352 video displayed on an 80" TV will look good, but I assume you're probably watching this on a computer or substantially smaller set.
I just went to youtube and checked your video out. There's some noise, color bleed, fading, etc. but I set youtube to 480 and it seemed fine to me. I'm using a samsung ultrabook i7, with a 15" hd screen. I think the noise, etc. that I saw was in the recording. It could be that it was shot with tape(VHS, MiniDV, etc.) then was transferred from a tape to another tape. Each generational transfer with a medium like that creates noise similar to what I saw. But I don't think it's unviewable and in fact I thank you for your post as I didn't know about this video and am going to watch it now.